Rotations, step by step
A rotation turns a point about the origin, and the quarter turns are the ones with clean coordinate rules.
The question
90° counterclockwise about O ()
(2, −2) 90° counterclockwise about O
(2, −2)
2, −2swap−2, 2
(2, −2)→(2, 2)
- Start where the point is: (2, −2). The move is 90° counterclockwise about O, and the question is only where those two numbers end up.
- A quarter turn SWAPS the two numbers — going 2 across and −2 up becomes going −2 across and 2 up — and then one of them changes sign, because the turn carries the point into a different quarter of the grid.
- Turning counterclockwise, that gives (2, 2).
How it works.
- 01
Start where the point is: (2, −2). The move is 90° counterclockwise about O, and the question is only where those two numbers end up.
- 02
A quarter turn SWAPS the two numbers — going 2 across and −2 up becomes going −2 across and 2 up — and then one of them changes sign, because the turn carries the point into a different quarter of the grid.
- 03
Turning counterclockwise, that gives (2, 2).